The subject of this presentation is the application of mathematical methods by means of which an optical resonator can be synthesized according to a pre-required profile shape, using either phase, amplitude or complex graded optical elements. If the profile is imposed on the transverse co-ordinates at a given plane inside the resonator, a matrix formalism based on the orthogonal collocation method is used. One main outcome of this research is the role of saturable gain on the mode shape attained. Examples of applications of these techniques toward the improved performance of solid state lasers are presented, specifically, the matching of modes to rod solid amplifying media. The synthesis of modes is demonstrated by means of several reflectivity grading options. These options are compared according to their ability to discriminate between the desired mode and other modes supported by the same optical structure.